List of top Instrumentation and Process Control Questions on Transfer functions and dynamic responses of various systems

For the block diagram shown in the figure, the correct expression for the transfer function \( G_d = \frac{y_1(s)}{d(s)} \) is:

A cascade control strategy is shown in the figure. The transfer function between the output \((y)\) and the secondary disturbance \((d_2)\) is defined as \(G_{d2}(s)=\dfrac{y(s)}{d_2(s)}\). Which one of the following is the CORRECT expression for \(G_{d2}(s)\)?

A measuring instrument has transfer function \[ G_m(s)=\frac{1.05}{2s+1}\,e^{-s}. \] At \(t=0\), a step of \(+1\) unit is applied. Find the time taken for the output to increase by \(1\) unit.

Level (\(h\)) in a steam boiler is controlled by manipulating the flow rate (\(F\)) of the make-up water using a proportional (P) controller. The transfer function is \[ \frac{h(s)}{F(s)} = \frac{0.25(1-s)}{s(2s+1)}. \] The measurement and valve transfer functions are both 1. A process engineer wants the closed-loop response to give decaying oscillations under servo mode. Which one of the following is the CORRECT value of the controller gain?

A liquid surge tank has \(F_{in}\) and \(F_{out}\) as the inlet and outlet flow rates respectively, as shown in the figure. \(F_{out}\) is proportional to the square root of the liquid level \(h\). The cross-sectional area of the tank is \(20~\text{cm}^2\). Density of the liquid is constant everywhere in the system. At steady state, \(F_{in}=F_{out}=10~\text{cm}^3\text{s}^{-1}\) and \(h=16~\text{cm}\). The variation of \(h\) with \(F_{in}\) is approximated as a first-order transfer function. Which one of the following is the CORRECT value of the time constant (in seconds) of this system?

Consider a single-input-single-output (SISO) system with the transfer function \[ G_p(s)=\frac{2(s+1)}{\left(\frac{1}{2}s+1\right)\left(\frac{1}{4}s+1\right)} \] where the time constants are in minutes. The system is forced by a unit step input at time $t=0$. The time at which the output response reaches its maximum is \(\underline{\hspace{2cm}}\) minutes (rounded off to two decimal places).

A process described by the transfer function \[ G_p(s) = \frac{10s + 1}{5s + 1} \] is forced by a unit step input at time $t = 0$. The output value immediately after the step input (at $t = 0^+$) is \(\underline{\hspace{2cm}}\) (rounded off to the nearest integer).

A system has a transfer function
\[ G(s) = \frac{3e^{-4s}}{12s^2 + 1} \] When a step change of magnitude M is given to the system input, the final value of the system output is measured to be 120. The value of M is \(\underline{\hspace{1cm}}\) .

A process has a transfer function
\[ G(s) = \frac{Y(s)}{X(s)} = \frac{20}{90000s^2 + 240s + 1} \] Initially the process is at steady state with \( x(t = 0) = 0.4 \) and \( y(t = 0) = 100 \). If a step change in \( x \) is given from 0.4 to 0.5, the maximum value of \( y \) that will be observed before it reaches the new steady state is \(\underline{\hspace{1cm}}\) (round off to 1 decimal place).